The product of a non-zero rational

Question:

The product of a non-zero rational and an irrational number is

(a) always irrational                                  

(b) always rational

(c) rational or irrational                            

(d) one

Solution:

(a) Product of a non-zero rational and an irrational number is always irrational i.e.,

$\frac{3}{4} \times \sqrt{2}=\frac{3 \sqrt{2}}{4}$ (irrational).

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